Finally, we consider the ability of current extragalactic gamma-ray data to constrain our model's parameters. For this we consider the extragalactic gamma-ray background (EGB) measured by the Fermi-Large Area Telescope (LAT) [1]}. In order to place conservative bounds we adopt the published EGB spectrum under the assumption of LAT's Galactic foreground model B, the foreground model which attributes the least Galactic emission to the measured gamma-ray flux. We consider a model to be excluded if its predicted gamma-ray flux exceeds the EGB model B measurement by more than the error bar in any energy bin. In plots we also give an estimate of the truly diffuse gamma-ray background (TDGRB) – as described in Section 2 of [2]} – and the flux measured in the highest energy bin of the isotropic gamma-ray background (IGRB) model B by LAT [1]}. As is shown in Fig. REF , gamma-ray data is weakly constraining, only ruling out models already excluded by bounds on EHE neutrinos. Thus we set aside the gamma-ray constraints for the rest of our analysis.
